Tyrion approved of his sister’s choice of Ser Balon Swann to take the place of the slain Preston Greenfield… In addition to being well born, young Ser Balon was valiant, courtly, and skilled at arms; good with a lance, better with a morningstar, superb with the bow. He would serve with honor and courage.

Ser Balon is the most honorable of the Kingsguard, the only one Jaime considers a benefit to the Kingsguard.

Jaime turned to Ser Balon Swann. “Ser Balon, I have watched you tilt many a time, and fought with and against you in melees. I’m told you proved your valor a hundred times over during the Battle of the Blackwater. The Kingsguard is honored by your presence.”

Something of a war hero, he was quite heroic during the battle of the Blackwater, where he fought alongside Tyrion.

His two white shadows were always with him; Balon Swann and Mandon Moore, beautiful in their pale plate. Surrounded by a circle of Velaryon spearmen, they fought back to back; they made battle as graceful as a dance.

Later, he is the only other of the Kingsguard to continue to believe Tyrion is innocent.

More recently, though, he has been given a task of immense dishonor.

Prince Doran took a jagged breath. "Dorne still has friends at court. Friends who tell us things we were not meant to know. This invitation Cersei sent us is a ruse. Trystane is never meant to reach King's Landing. On the road back, somewhere in the kingswood, Ser Balon's party will be attacked by outlaws, and my son will die. I am asked to court only so that I may witness this attack with my own eyes and thereby absolve the queen of any blame. Oh, and these outlaws? They will be shouting, 'Halfman, Halfman,' as they attack. Ser Balon may even catch a quick glimpse of the Imp, though no one else will."

Jaime Lannister is vanished. Tyrion Lannister has vanished. Tywin Lannister is dead. Ser Balon Swann works for Cersei now, and she has no idea the kind of man he is.

He is so uncomfortable with the mission that even Areo can see it immediately, although Areo does instinctively feel that Ser Balon is somewhat of a threat.

Ser Balon gave a nod and sipped his wine. This one is not so easily seduced as was his Sworn Brother, Hotah thought. Ser Arys was a boy, despite his years. This one is a man, and wary. The captain had only to look at him to see that the white knight was ill at ease.

Perhaps there is some mystery with Ser Balon’s mission. But if so, it is rather an unfair mystery, as we hear Cersei corroborate that Ser Balon has a secret mission.

"To be sure." A tiresome creature, this prince. "His long wait is almost done. I am sending Balon Swann to Sunspear, to deliver him the head of Gregor Clegane." Ser Balon would have another task as well, but that part was best left unsaid.

In fact, saner voices on Prince Doran’s side have advocated that Ser Balon be disposed of. After all, even if they can compel Myrcella to lie for now, she’ll tell the truth about the Queenmaker plot eventually.

"It is all true," said the prince, with a wince of pain. Is it his gout that hurts him, or the lie? "And now Ser Gerold has fled back to High Hermitage, beyond our reach."

"Darkstar," Tyene murmured, with a giggle. "Why not? It is all his doing. But will Ser Balon believe it?"

"He will if he hears it from Myrcella," Arianne insisted.

Obara snorted in disbelief. "She may lie today and lie tomorrow, but soon or late she'll tell the truth. If Ser Balon is allowed to carry tales back to King's Landing, drums will sound and blood will flow. He should not be allowed to leave."

But Doran Martell doesn’t choose this option. Doran seemingly bets everything on Ser Balon behaving just like Areo Hotah and accepting the mission to hunt down Darkstar. But we have seen men break oaths, many for the best of reasons. I think Doran suspects, correctly, that Ser Balon may soon break his.

Consider that Ser Balon chose to accept Princess Myrcella’s request to hunt down her attacker. He was not ordered to obey her, just to bring her back to Cersei and kill Trystane. Hunting down an outlaw in the Red Mountains of Dorne was not the plan, and would take weeks, if not months. These are not his orders, and obeying a command from Myrcella does not justify delaying returning her to Cersei.

In fact, Jaime specifically gave his Kingsguard advice on not obeying orders from children.

Ser Meryn got a stubborn look on his face. "Are you telling us not to obey the king?"

"The king is eight. Our first duty is to protect him, which includes protecting him from himself. Use that ugly thing you keep inside your helm. If Tommen wants you to saddle his horse, obey him. If he tells you to kill his horse, come to me." "Aye. As you command, my lord."

Ser Balon perhaps accepted the mission to hunt down Darkstar in an effort to avoid his dishonorable task as long as possible, and maybe altogether. I suspect that he even perhaps hoped to perish nobly in battle against Myrcella’s would-be assassin instead of following through on the plot to murder Trystane, as he had been ordered.

The point is this: Ser Balon should be looking for any excuse to forswear his loyalty to the Lannisters. Lord Tywin, who Ser Balon fought for on the Blackwater, is dead. Tyrion, Ser Balon’s War buddy, killed his king. Jaime, who he respected somewhat, has vanished. Loras has been mutilated. Cersei Lannister is commanding him to murder children. His two remaining Kingsguard brothers are Osney Kettleblack and Meryn Trant.

There is an opportunity for him to do so, and to do so with honor.

A look at his family circumstances is warranted:

The Swanns were Marcher lords, proud, powerful, and cautious. Pleading illness, Lord Gulian Swann had remained in his castle, taking no part in the war, but his eldest son had ridden with Renly and now Stannis, while Balon, the younger, served at King’s Landing. If he’d had a third son, Tyrion suspected he’d be off with Robb Stark. It was not perhaps the most honorable course, but it showed good sense; whoever won the iron Throne, the Swanns intended to survive.

Lord Commander Jaime Lannister interrogates Ser Balon on this point, family loyalty being the only thing Jaime can imagine swaying Ser Balon from his duty. It is important to consider the following exchange in light of present circumstances.

“There is only one question I would put to you. You served us loyally, it’s true... but Varys tells me that your brother rode with Renly and then Stannis, whilst your lord father chose not to call his banners at all and remained behind the walls of Stonehelm all through the fighting.”

“My father is an old man, my lord. Well past forty. His fighting days are done.”

“And your brother?”

“Donnel was wounded in the battle and yielded to Ser Elwood Harte. He was ransomed afterward and pledged his fealty to King Joffrey, as did many other captives.”

“So he did,” said Jaime. “Even so... Renly, Stannis, Joffrey, Tommen how did he come to omit Balon Greyjoy and Robb Stark? He might have been the first knight in the realm to swear fealty to all six kings.”

Ser Balon’s unease was plain. “Donnel erred, but he is Tommen’s man now. You have my word.”

“It’s not Ser Donnel the Constant who concerns me. It’s you.” Jaime leaned forward. “What will you do if brave Ser Donnel gives his sword to yet another usurper, and one day comes storming into the throne room? And there you stand all in white, between your king and your blood. What will you do?”

“I… my lord, that will never happen.”

“It happened to me,” Jaime said.

Swann wiped his brow with the sleeve of his white tunic.

“You have no answer?”

“My lord.” Ser Balon drew himself up. “On my sword, on my honor, on my father’s name, I swear... I shall not do as you did.”

I suspect in the near future, Ser Donnel Swann and Lord Swann will indeed be switching sides again. Aegon Targaryen, having raised up his banner over Storm’s End, will be marching on King’s Landing, and noble knights and great lords  will be flocking to his cause. Lord Swann, and Ser Donnel, will pledge themselves to his cause.

"Has no one told you?" Halden Halfmaester favored her with a smile thin and hard as a dagger cut. "Storm's End is ours. The Hand awaits you there."

Lord Gulian Swann owes his fealty to Storm’s End, yet has kept his levies at home throughout the War of the Five Kings. His men are fresh, trained, and ready whereas many other houses have been depleted. Likely this is justified by the two Dornish armies in the Boneway and the Prince’s Pass. But the Swann levies could be raised if those armies marched out on behalf of Aegon.

Ser Balon, meanwhile, might hear of this at High Hermitage or, more likely, Starfall. And he will indeed be faced with Jaime’s choice. My father or my king. In light of what staying loyal to Cersei means for him (murdering children, apparently), I believe he will see it as his only escape and choose to defect.

A solid man, and true, Connington thought as he watched Duck dismount, but not worthy of the Kingsguard. He had tried his best to dissuade the prince from giving Duckfield that cloak, pointing out that the honor might best be held in reserve for warriors of greater renown whose fealty would add luster to their cause, and the younger sons of great lords whose support they would need in the coming struggle, but the boy would not be moved.

Notably, knights of the Kingsguard have defected during wars with multiple strong claimants. Aegon II and Rhaenyra had such Kingsguard.

Aegon II had suffered his first defections the night before, when Ser Steffon Darklyn of the Kingsguard had slipped from the city with his squire, two stewards, and four guardsmen. Under the cover of darkness they made their way out a postern gate to where a fisherman’s skiff awaited to take them to Dragonstone. They brought with them a stolen crown: a band of yellow gold ornamented with seven gems of different colors. 

Though Aegon named them turn cloaks, they were accepted by Rhaenyra, who saw them as loyal men and a credit to her cause.

 The arrival of Ser Steffon Darklyn, late of Aegon’s Kingsguard, was an occasion of much joy on Dragonstone, especially when it was learned that he and his fellow loyalists (“turncloaks,” Ser Otto would name them, when offering a reward for their capture) had brought the stolen crown of King Jaehaerys the Conciliator. Three hundred sets of eyes looked on as Prince Daemon Targaryen placed the Old King’s crown on the head of his wife, proclaiming her Rhaenyra of House Targaryen, First of Her Name, Queen of the Andals, the Rhoynar, and the First Men. 

In some senses, Ser Balon Swann is the most prominent Kingsguard in the story other than Jaime Lannister. He is one of only four characters in the Hotah plot, which has quickly become The Good, the Bad, and the Ugly. So there is something coming with him. I believe he will try to get out from under.

(The same plan, of course, is even more in the interest of the fugitive Darkstar — with Doran and Cersei both trying to murder him, where else can Ser Gerold turn for safety? Rhaegar’s son could use an Arthur Dayne of his own.)

TL;DR; Balon Swann is an honorable man, and will defect to Aegon VI instead of going through with his orders to kill Trystane.